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Simplify Fractions Calculator

Shrink a fraction to its simplest form with every step shown, see fractions that are worth the same, and check whether two fractions are equal.

Level: Grades 4–6

  • Common Core standard 4.NF.A.1Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
  • Common Core standard 6.NS.B.4Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor.
Printable worksheet

Simplify Fractions Calculator

Inputs
Calculation

A whole number other than zero.

Result

Simplified fraction

3/4

18/24 simplifies to 3/4.

Greatest common divisor
6
Decimal value
0.75

See the step-by-step solution ↓

Fractions equivalent to 3/4 (multiply the top and bottom by the same number)
Fractions equivalent to 3/4 (multiply the top and bottom by the same number)
Multiply byEquivalent fraction
26/8
39/12
412/16
515/20
618/24
721/28
824/32
927/36
1030/40

Step-by-step solution

  1. Find the biggest number that divides both the top and bottom evenly, called the GCD. Divide, keep what's left over, and repeat until nothing is left

    GCD(18, 24)

  2. 24 ÷ 18 leaves 6 left over

    24=1×18+6

  3. Nothing is left over, so the last number you divided by, 6, is the GCD

    18=3×6+0

  4. Divide the top and bottom by the GCD, 6, to get the simplest form

    18÷624÷6=34

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Turn a fraction like 18/24 into its simplest form, 3/4, and see exactly how it's done. A fraction is in lowest terms when its top and bottom numbers can't both be divided by anything bigger than 1. The top number is the numerator and the bottom is the denominator. 18/24 and 3/4 are the same amount, but 3/4 is easier to read, compare and work with.

To simplify, you find the largest number that divides both parts evenly. That's the greatest common divisor (GCD). Then you divide both parts by it. The calculator finds the GCD with a classic shortcut called the Euclidean algorithm, and it shows every division so you can follow along by hand. It also lists fractions worth the same as your answer. A second mode tells you whether two fractions are equal by comparing their cross products.

Where it's used

Why this math matters outside the classroom:

  • Measuring cups. A cook reduces 6/8 cup to 3/4 cup to find it among standard measuring cups.
  • Test scores. A student who got 18 of 24 right simplifies 18/24 to 3/4, three quarters of the questions.
  • Gear ratios. A mechanic writes 36 teeth to 48 teeth as 3/4 by dividing both numbers by their GCD, 12.
  • Card odds. Drawing a heart from a 52-card deck has probability 13/52, which simplifies to 1/4.
  • Ruler marks. A woodworker measures 10/16 of an inch and reads it as 5/8 on a ruler marked in eighths.

Grade level and standards: Grades 4–6; Common Core State Standards for Mathematics 4.NF.A.1, 6.NS.B.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Choose whether to simplify one fraction or check two fractions against each other.
  2. Enter whole numbers for the top numbers, and whole numbers other than zero for the bottom numbers. Negative numbers are fine.
  3. Read the simplified fraction or the yes-or-no answer. Then open the steps to see the working.
  4. In simplify mode, use the table of equivalent fractions when you need a particular bottom number.

What the inputs mean

Numerator
The top number. Zero is allowed, and it simplifies to 0.
Denominator
The bottom number. It can't be zero. If it's negative, the minus sign moves to the top number.
Second numerator
The top number of the fraction you're comparing against.
Second denominator
The bottom number of the fraction you're comparing against. It can't be zero.

Formula and method

g = GCD(|a|, |b|)
a/b = (a ÷ g) / (b ÷ g)
Euclid: GCD(x, y) = GCD(y, x mod y), and GCD(x, 0) = x
a/b = c/d  ⇔  a × d = b × c
Equivalent fractions: a/b = (a × m) / (b × m) for any whole m ≠ 0

In the formulas, a/b is your fraction: a is the top number and b is the bottom. c/d is the second fraction in check mode. g is the GCD, and |a| means a without its minus sign. "x mod y" means the remainder when you divide x by y. m is any whole number except zero, and ⇔ means "exactly when".

Dividing the top and bottom by the same number never changes a fraction's value. Dividing by the GCD removes every shared factor in one go. So the result is sure to be in lowest terms.

The Euclidean algorithm finds the GCD without listing factors. Divide the larger number by the smaller one and keep the remainder. Next, take the number you just divided by, and divide it by that remainder. Keep going the same way. When the remainder reaches 0, the last number you divided by is the GCD.

To compare two fractions, multiply each top number by the other fraction's bottom number. These are the cross products. If they match, the fractions are equal. It's the same as rewriting both fractions over one shared bottom number, b × d.

Worked example

A survey found that 18 of 24 people preferred the morning class. What fraction is that in lowest terms?

  1. Find the GCD of 18 and 24 with the Euclidean algorithm. First, 24 = 1 × 18 + 6, so the remainder is 6.
  2. Next: 18 = 3 × 6 + 0. The remainder is 0, so the GCD is 6.
  3. Divide both parts by 6: 18 ÷ 6 = 3 and 24 ÷ 6 = 4.
  4. Fractions worth the same include 6/8, 9/12 and 30/40.
  5. Checking 18/24 against 15/20: 18 × 20 = 360 and 24 × 15 = 360, so they're equivalent.

Result: 18/24 simplifies to 3/4 (GCD 6, decimal 0.75).

Understanding the result

If the GCD is 1, the fraction was already in lowest terms, and the calculator tells you so.

The simplified answer always has a positive bottom number. Any minus sign goes on the top, so 6/−8 is shown as −3/4.

In check mode, 'Equivalent' means the two fractions are exactly equal in value, not just close.

Assumptions and limitations

  • You enter whole numbers. To simplify a fraction with decimals, such as 1.5/4.5, first multiply both parts by 10 to get 15/45.
  • The equivalent fractions in the table are the simplified fraction with its top and bottom multiplied by the same whole number.
  • Simplifying takes numbers up to 1,000,000,000,000 in size. Checking two fractions takes numbers up to 10,000,000, so the cross products stay exact.
  • The steps show up to eight divisions of the Euclidean algorithm and sum up any beyond that.

Frequently asked questions

Do I have to use the greatest common divisor?

No. You can divide by any number that goes into both and repeat. For example, 18/24 → 9/12 → 3/4 by dividing by 2 and then by 3. Using the GCD just gets there in one step, and it makes sure nothing is left to divide out.

How do I know a fraction can't be simplified further?

When the GCD of the top and bottom numbers is 1. That's why two whole numbers in a row, such as 8/9, are always in lowest terms.

Why does cross-multiplication show that two fractions are equal?

Rewrite both fractions over the shared bottom number b × d. Then a/b becomes (a × d)/(b × d), and c/d becomes (b × c)/(b × d). With the same bottom number, the fractions are equal exactly when the top numbers, a × d and b × c, are equal.

Is a negative fraction simplified differently?

No. The minus sign is set aside, and the GCD of the numbers without their signs is divided out. Then the sign goes back on the top number. −12/18 and 12/−18 both simplify to −2/3.

How this calculator is checked

Method: Reduction by the greatest common divisor, computed with the Euclidean algorithm; equality of fractions by cross-multiplication. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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